We construct a primitive gate set for the digital quantum simulation of the 48-element binary octahedral ($\mathbb{BO}$) group. This non-Abelian discrete group better approximates $SU(2)$ lattice gauge theory than previous work on the binary tetrahedral group at the cost of one additional qubit—for a total of six—per gauge link. The necessary primitives are the inversion gate, the group multiplication gate, the trace gate, and the $\mathbb{BO}$ Fourier transform.

• Received 2 January 2024
• Accepted 13 February 2024

DOI:https://doi.org/10.1103/PhysRevD.109.054503

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Published by the American Physical Society